Power systems are going through a paradigm change from centralized generation to distributed generation. More and more distributed energy resources (DERs), including renewables, electric vehicles, and energy storage systems, are being integrated into the grid. The integration of DERs presents unprecedented challenges and has become an important research topic in recent years. One challenge is that a DER unit often means low inertia or even inertia-less. The large-scale utilization of DERs would cause significant decrease of inertia, which brings considerable concerns about grid stability, because inertia has been regarded as a critical factor for guaranteeing the stability of power systems.
Since synchronous machines (SM) can provide large inertia because of the large kinetic energy stored in the rotors, a lot of efforts have been made in recent years to provide additional energy when needed to mimic the inertia. For example, a fast-response battery energy storage system can be adopted to inject additional power when needed. The inertia of a PV system can be increased by adjusting the DC-link voltage and the PV array output. The kinetic energy stored in the rotor of a wind turbine can be utilized for wind plants to participate in system frequency regulation.
Another important trend is to operate power electronic converters in DER units as virtual synchronous machines (VSM), which are power electronic converters that emulate the major features of a traditional SM, such as torque, inertia, voltage, frequency, phase, and field-excitation current. VSMs have become the building blocks for future power electronics-enabled autonomous power systems, which are characterized as synchronized and democratized (SYNDEM) smart grids. Different/similar options to implement VSMs have been proposed in the literature. The VISMA approach controls the inverter current to follow the current reference generated according to the mathematical model of SM, which makes inverters behave like controlled current sources. The synchronverter (SV) approach or the static synchronous generator disclosed in US 2011/0270463 A1 directly embeds the mathematical model of SM into the controller to control the voltage generated. The conventional inertia factor J and damping factor Dp of an SM are emulated through embedding the swing equation of SM in the controller. US 2014/0067138 A1 discloses a virtual controller of electromechanical characteristics for static power converters, which adopts a power loop controller with the capability of adjusting the inertia factor and the damping factor. The power loop controller is actually equivalent to the swing equation of SM. CN106208159A discloses a virtual synchronous machine-based dynamic power compensation method, which also adopts the swing equation of SM as the core of the controller but with the additional feature of adjusting the inertia factor and the damping factor according to the variation of the frequency. CN107154636A discloses a multi-target optimization control method, which also incorporates the swing equation of SM as the basis of the controller for optimization. In summary, a common feature of the state of the art about VSM is to incorporate the swing equation of SM and adjust the inertia factor and the damping factor accordingly. However, as to be shown later, the virtual inertia that can be provided by the swing equation of an SM is limited. Moreover, the frequency response of a VSM can be oscillatory when the virtual inertia increases. Furthermore, the output current of such a VSM can be excessive when a grid fault occurs, making it difficult to ride-through grid faults.